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SUBGEOMETRICALLY ERGODIC AUTOREGRESSIONS WITH AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY

Published online by Cambridge University Press:  17 November 2023

Mika MeitzOpen the ORCID record for Mika Meitz[Opens in a new window] and
Pentti Saikkonen
Mika Meitz*
Affiliation:
University of Helsinki
Pentti Saikkonen
Affiliation:
University of Helsinki
*
Address correspondence to Mika Meitz, Department of Economics, University of Helsinki, P. O. Box 17, FI-00014 University of Helsinki, Finland; e-mail: mika.meitz@helsinki.fi.
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Abstract

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In this paper, we consider subgeometric (specifically, polynomial) ergodicity of univariate nonlinear autoregressions with autoregressive conditional heteroskedasticity (ARCH). The notion of subgeometric ergodicity was introduced in the Markov chain literature in the 1980s, and it means that the transition probability measures converge to the stationary measure at a rate slower than geometric; this rate is also closely related to the convergence rate of $\beta $-mixing coefficients. While the existing literature on subgeometrically ergodic autoregressions assumes a homoskedastic error term, this paper provides an extension to the case of conditionally heteroskedastic ARCH-type errors, considerably widening the scope of potential applications. Specifically, we consider suitably defined higher-order nonlinear autoregressions with possibly nonlinear ARCH errors and show that they are, under appropriate conditions, subgeometrically ergodic at a polynomial rate. An empirical example using energy sector volatility index data illustrates the use of subgeometrically ergodic AR–ARCH models.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 41 , Issue 1 , February 2025, pp. 218 - 248
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Footnotes

The authors thank the Academy of Finland (M.M. and P.S.), Foundation for the Advancement of Finnish Securities Markets (M.M.), and OP Group Research Foundation (M.M.) for financial support, and the Co-Editor (Robert Taylor) and three anonymous referees for useful comments and suggestions.

References

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